The correct answer is:
The statement is false, because the lines have an intersection point.
To solve the system by graphing, we can plot the two given equations on a coordinate plane and see where the lines intersect.
The first equation, y = -x + 3, has a slope of -1 and a y-intercept of 3. This means that if we start at the point (0, 3), we can move down 1 unit and right 1 unit to find another point on the line. Similarly, if we start at (0, 3), we can move up 1 unit and left 1 unit to find another point.
The second equation, x + y = 8, can be rewritten as y = -x + 8. This equation also has a slope of -1, but a y-intercept of 8. So, if we start at the point (0, 8), we can move down 1 unit and right 1 unit to find another point on the line. Also, if we start at (0, 8), we can move up 1 unit and left 1 unit to find another point.
Graphing the two lines, we can see that they intersect at the point (2, 6). Therefore, there is a solution to the system, and the statement is false.
Solving the system y=−x+3 and x+y=8 by graphing shows that there is no solution to the system. Is this statement true or false? Explain. %0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AThe statement is true, because the lines are parallel.%0D%0AThe statement is true, because the lines are parallel.%0D%0A%0D%0AThe statement is false, because the lines have an intersection point.%0D%0AThe statement is false, because the lines have an intersection point.%0D%0A%0D%0AThe statement is true, because the lines have an intersection point.%0D%0AThe statement is true, because the lines have an intersection point.%0D%0A%0D%0AThe statement is false, because the lines are parallel.
1 answer